Here are some irregular adverbs that defy the rules set up in this post.
diū, diūtius, diūtissimē, for a long time, for a longer time, for the longest time
potius, ——potissimum, rather, first of all
saepe, saepius,saepissimē, often, more often/again, most often
satis, satius, —— enough, preferable
secus, sētius, —— otherwise, worse
multum (or multō), magis (or mage), maximē, much, more, most
parum, minus, minimē, not enough, less, least
nūper, ——, nūperrimē, newly, most newly
temperē, temperius, —— seasonably, more seasonably
Most of these are either disconnected from their corresponding adjectives (semantically), or are defective in either comparative or superlative form. However, the real outlier here is the multum/ō, magis/e, maximē set, which is an aggregate of various options. Multō is of course the ablative singular neuter for the positive adjective, and mage the neuter accusative of the comparative adjective.
Magis and maximē may also be paired with other adjectives to create their comparatives, especially in adjectives ending in -eus or -ius (in the positive.)
idōneus, magis idōneus, maximē idōneus, fit, more fit, most fit